They are not exact at all, but only approximations of the real world. Hacks, if you will. :)

For more "exact approximations" (amusingly paradoxical expression eh?), you might want to have a look at global illumination algorithms.

They say the most accurate clock is a broken one. Because a broken clock is exactly precise, with no error whatsoever, once or twice a day; but, a working clock cannot track time with no error and so runs too fast or lags slightly, only to catch up and be exact for one moment every....century or so.

In a sense, the Lambert and Phong lighting models are like that broken clock. For some material types at certain view angles (view angles that are instantly reproducable in a 3D sim), they probably produce exactly the precisely correct answer (well, there would be floating point roundoff error at least in a numerical simulation).

Other than that, you may want to study BRDF theory, to learn about how the various approximations relate to real-world materials (BRDF being something that can be measured using sensors for real-world materials).